Improved bounds for the total variation distance between stochastic polynomials
Egor Kosov, Anastasia Zhukova
TL;DR
This paper provides improved upper bounds for the total variation distance between certain polynomial functions of random vectors, leveraging recent advances in the smoothness of their distribution densities.
Contribution
It introduces tighter bounds for the total variation distance between polynomials of special form in random vectors under Doeblin-type conditions, improving previous estimates.
Findings
Enhanced bounds for total variation distance
Application of Nikolskii--Besov-type smoothness results
Improved estimates over previous work
Abstract
The paper studies upper bounds for the total variation distance between two polynomials of a special form in random vectors satisfying the Doeblin-type condition. Our approach is based on the recent results concerning Nikolskii--Besov-type smoothness of distribution densities of polynomials in logarithmically concave random vectors. The main results of the paper improve previously obtained estimates of Nourdin--Poly and Bally--Caramellino.
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Taxonomy
TopicsPoint processes and geometric inequalities · Bayesian Methods and Mixture Models